Satellite radio navigation offers wide-range and precise positioning services with guaranteed reliability, thanks to the state-of-the-art technologies adopted by the existing GPS system. In a few years time, these will be further enhanced by the introduction of the European Galileo satellite navigation constellation, an initiative launched by the European Union and the European Space Agency (ESA). Galileo along with the upcoming third generation GPS III are expected to ensure wider coverage and more precise time and location positioning facilities. However, ensuring such services requires careful reconsideration of different navigation signal parameters such as modulation scheme, navigation message structure and spreading codes design.
The use of spreading codes makes signals appear wide band and noise-like. It is this very characteristic that makes these signals difficult to intercept, hard to jam and unlikely to interfere with narrowband signals. Therefore, spreading codes play an important role in ensuring a reliable and secure transmission, without producing significant interference with other signals. In spread-spectrum multiple access transmission, such as Direct Sequence Code Division Multiple Access (DS-CDMA) and satellite navigation systems, different signals are assigned different codes and the receiver recovers the desired user's signal by making use of the knowledge of the corresponding spreading code. These spreading codes are desired to have delta-peak-like autocorrelations for an accurate synchronization and low cross-correlations in order to reduce co-channel interferences. Conventional Linear Feedback Shift Register (LFSR) sequences are the most known and studied pseudo-random binary codes in literature and largely used in various applications such as DS-CDMA and satellite navigation systems.
With regard to the future Galileo satellite navigation system, there is a need to generate new codes in addition to the baseline codes already described in the SIS ICD [1] and assessed in Phase C0 document [2]. Assessment of the baseline codes will require direct comparison with other codes and code sets. Most of the codes described previously, such as the existing E5 Galileo codes, suffer from problems due to truncation from their maximal length. Thus, one should generate codes which have maximal length that is not restricted to a value 2N−1, for some N. Many codes have been proposed which, in theory, may outperform standard linear feedback shift register-based codes. Thus these codes are worthy of investigation as potential alternatives to the baseline codes, and may be considered for deployment in a flexible Galileo architecture.
The baseline Galileo codes, are either memory or combined and truncated maximum length sequences (m-sequences). Undeniably, m-sequences are easy to be generated and possess perfect autocorrelation behavior. However, besides the typical moderate cross-correlation performance of m-sequences, the truncation process, required to ensure the desired code length, destroys the perfect autocorrelation behavior of such sequences and has an adverse effect on their performance. Conversely, the memory codes can be optimized to have better performance but are difficult to generate on-chip in real-time and hence have to be stored in memory. Therefore, the investigation of alternative schemes such as chaotic codes, which could offer better performance and ease of implementation, would certainly be in the interest of the spread spectrum community.
One of the problems with pseudo-random codes is their generation. The PRN codes generated by digital signal processors tend to be periodic due to the digital nature of the processors. There has been significant interest in recent years in exploiting chaotic generators to create spreading codes in Spread Spectrum systems [3-5]. The simplicity of these generators, the non-periodicity of the chaotic signals, their sensitivity to initial conditions and their flexibility in terms of length make these generators of significant interest in utilization e.g. in satellite navigation technology or communication technology. These chaotic codes have the benefits of simple implementation, broadband and noise-like appearance, improved transmission privacy, especially over standard m-sequences and Gold sequences, and robustness against channel imperfections like multipath propagation and jamming [3, 4]. Furthermore, the inclusion of chaotic code implementations which are not based on shift registers allows one to generate spreading codes of arbitrary length without the need for truncation. Recent results [5, 8-10] have demonstrated that suitable spreading code generators, based on chaotic maps, may be generated robustly and efficiently, in digital hardware. The high performance of such maps was investigated in [11], where it was also shown how these maps may be modified to yield near ideal correlation properties. Furthermore, the concept of the utilization of chaotic sequences with finite bits by means of a linear feedback shift register has been realized in [8-10] and an algorithmic approach of how to design a decimal m-sequence with prescribed autocorrelation function has been described in [11].
However, these studies are only suitable for maximal length sequences and are not suitable to arbitrary length codes such as found in Galileo. In fact, extensive simulations have been carried out, where numerous chaotic sets, based on above studies, have been generated and assessed. Despite the good autocorrelation behavior of such chaotic codes, the random process used in selecting these codes has caused unacceptably weak cross-correlation performance. Furthermore, Gold and Kasami strategies have been to overcome this drawback, however, since these two methods were initially proposed for m-sequences and not for chaotic codes, both failed to provide satisfactory cross correlation performance.